Two equal sums are lent at 10% and 8% simple interest p.a. respectively, at the same time. The first sum is received 2 years earlier than the second one and the amount received in each case was ₹36,900. Each sum was

Let the principle amount be P and the time for first sum be x years.

Time for second sum = x + 2

Rate for first sum = 10%

Rate for second sum = 8%

Amount = $$\frac{P \times rate \times time}{100} + P$$

$$\frac{P \times 10 \times x}{100} + P$$ =  $$\frac{P \times x \times (x + 2)}{100} + P$$

10x = $$x^2 $$+ 2x

$$x^2 - 8x = 0$$

x(x - 8) = 0

x = 8

Amount for the fist sum = $$\frac{P \times rate \times time}{100} + P$$

36900 = $$\frac{P \times 10 \times 8}{100} + P$$

36900 = $$\frac{180P}{100}$$

P = 20500

Each sum = Rs.20500